Affine One-Wayness: Post-Quantum Temporal Verification via Polynomial Iteration ∞ Research

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Briefing

Distributed systems face a critical challenge in establishing verifiable temporal ordering without relying on trusted authorities or synchronized clocks. This research introduces Affine One-Wayness (AOW), a novel cryptographic primitive that enables transparent post-quantum temporal verification through iterative polynomial evaluation over finite fields. AOW’s security relies on the hardness of the discrete logarithm problem in high-genus hyperelliptic curves and the Affine Iterated Inversion Problem, offering robust guarantees against classical and quantum adversaries. This new primitive profoundly impacts blockchain architecture by providing a foundational component for Byzantine-resistant event ordering and distributed synchronization, crucial for future scalable and secure decentralized applications.

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Context

Prior to this research, distributed systems grappled with the inherent difficulty of establishing a universally verifiable and tamper-proof temporal order for events. Traditional approaches often relied on centralized authorities, synchronized clocks, or computationally intensive consensus mechanisms, introducing vulnerabilities, scalability bottlenecks, or trust assumptions. The emergence of quantum computing further exacerbated this challenge, threatening the security foundations of existing cryptographic primitives used for timestamping and ordering, necessitating a robust, post-quantum secure solution for verifiable temporal integrity.

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Analysis

Affine One-Wayness (AOW) is a new cryptographic primitive designed for post-quantum temporal verification. It operates by performing iterative polynomial evaluation over finite fields. The core mechanism involves a one-way function where computing the forward iteration is efficient, but reversing it is computationally intractable, even for quantum adversaries.

This one-way property, combined with its affine structure, creates a verifiable “temporal binding.” AOW fundamentally differs from previous approaches by offering transparent setup and reducing its security to well-established hard problems in number theory and multivariate quadratic algebra, specifically the discrete logarithm problem in high-genus hyperelliptic curves and the Affine Iterated Inversion Problem. This allows for provable security guarantees without relying on interactive proofs or complex trusted setups, making it a foundational building block for secure temporal ordering in untrusted environments.

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Parameters

Core Concept ∞ Affine One-Wayness (AOW)
New Primitive ∞ Post-Quantum Temporal Verification
Security Basis ∞ Discrete Logarithm Problem in High-Genus Hyperelliptic Curves (HCDLP), Affine Iterated Inversion Problem (AIIP)
Underlying Mechanism ∞ Iterative Polynomial Evaluation over Finite Fields
Integration ∞ STARK Proof Systems
Key Authors ∞ MINKA MI NGUIDJOI Thierry Emmanuel
Framework ∞ Chaotic Affine Secure Hash (CASH)

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Outlook

This research opens new avenues for constructing truly asynchronous and Byzantine-resistant distributed systems. In the next 3-5 years, AOW could enable novel blockchain architectures that achieve verifiable event ordering and synchronization with unprecedented transparency and post-quantum security. Potential applications extend to highly resilient distributed ledgers, secure timestamping services, and verifiable computation systems that demand robust temporal integrity. Further research will likely explore optimizing AOW’s integration with various zero-knowledge proof systems and its broader applicability in privacy-preserving protocols, establishing a new paradigm for foundational trust in decentralized environments.

This research establishes a pivotal cryptographic primitive, Affine One-Wayness, fundamentally advancing the principles of verifiable temporal ordering and post-quantum security for future blockchain architectures.

Signal Acquired from ∞ IACR ePrint Report